Problem: Simplify the following expression: $8\sqrt{27}$.
Solution: First, try to factor a perfect square out of the radical. $= 8\sqrt{27}$ $= 8\sqrt{9 \cdot 3}$ Separate the radical and simplify. $= 8\sqrt{9} \cdot \sqrt{3}$ $= 8 \cdot 3 \cdot \sqrt{3}$ $= 24\sqrt{3}$